To become a founder of a Gang or a member, you have to extend your Saloon to level 4. Afterwards, you can build the Telegrpah Office next to your Bank. With a Telegraph Office you can start your gang careere.
Open up the Gang-menu by clicking on the Gang-button on the left. To become an Gang member you have to apply for membership first. Send your application via the profile of your chosen Gang. You can find Gangs by searching for them via the Gang search, or simply by clicking on scores and find them this way. If you wish, you can also apply for membership at several Gangs at once. After that, you need to wait if or when your membership-apply will be accepted.
Via the shift button in the Gang-menu you are able to found your own Gang.